Magnetic Deflection of Ionized Target Ions

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Magnus Fitzgerald
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1 Magnetic Deflection of Ionized Target Ions D. V. Rose, A. E. Robson, J. D. Sethian, D. R. Welch, and R. E. Clark March 3, 005 HAPL Meeting, NRL

2 Solid wall, magnetic deflection 1. Cusp magnetic field imposed on to the chamber (external coils). Ions compress field against the chamber wall: (chamber wall conserves flux) 3. Because these are energetic particles, that conserve canonical angular momentum (in the absence of collisions), Ions never get to the wall!! 4. Ions leak out of cusp ( 5 µsec), exit chamber through toroidal slot and holes at poles Coils Mag Field Particle Trajectory Toroidal Slot 5. Magnetic field directs ions to large area collectors 6. Energy in the collectors is harnessed as high grade heat Pole A.E. Robson, "Magnetic Protection of the First Wall," 1 June 003

3 J. Perkins calculated target ion spectra (9 th HAPL, UCLA, June -3, 004) Debris kinetic energy spectra Fast burn product escape spectra 3

4 Perkins combined ion spectra: Particle per unit energy (#/kev) 1E19 1E17 1E15 1E13 1E11 D T 4He H 3He He H 4He D T Particle Energy (kev) These energy spectra are sampled directly by LSP for creating PIC particles. 4

5 EMHD algorithm for LSP under Quasi-neutrality assumed Displacement current ignored development PIC ions (can undergo de/dx collisions) Massless electron fluid (cold) with finite scalar conductivity Only ion time-scales, rather than electron time-scales, need to be resolved. Model is based on previous work, e.g., Omelchenko & Sudan, JCP 133, 146 (1997), and references therein. Model used extensively for intense ion beam transport in preformed plasmas, ion rings, and field-reversed configurations. 5

6 EMHD model equations: Currents are source terms for curl equations: 4π B = j + j c B = c E t ( e i) Ohm s Law for electron fluid: E = + σ 1 e je j B ρ c e Scalar conductivity can be calculated from neutral collision frequencies: σ = ω 4π ν pe ( + ν ) ei en 6

7 Full-scale chamber simulations (PRELIMINARY RESULTS) 5-meter radius chamber, D (r,z) simulation 4 coil system for cusp B-field shape 10-cm initial radius plasma Perkins combined energy spectra for light ion species only (H +, D +, T +, 3 He ++, 4 He ++ ) cm -3 combined initial ion density (uniform)* * ~4.x10 0 ions represented by 5x10 5 macro-particles 7

8 Magnetic field maps: Coil configuration: r(cm) z(cm) I(MA)

9 Orbit Calculation ion positions at 500 ns Protons 4 Helium Ports at escape points in chamber added to estimate loss currents dz ~ 80 cm (width of slot) dr ~ 50 cm (radius of hole) 9

10 Preliminary EMHD simulations track magnetic field push during early phases of ion expansion. T = 0 T=500 ns 10

11 Ion Energy In Chamber vs. Time Orbit Calc., w/ Applied Field EMHD Calc., w/applied Fields Orbit-Calc., No Applied Fields 11

12 Escape Currents Cusp-field, slot No Applied Field, slot Cusp-field, hole No Field, hole 1

13 Status: Simulations using the Perkins target ion spectra: We have added a capability to LSP that loads ion energy spectra from tables EMHD model EMHD model has been added to LSP. Testing/benchmarking against simple models underway Results Preliminary EMHD simulations with 10 cm initial radius plasma volumes suggest that ions DO NOT STRIKE THE WALL during the first shock. Preliminary estimates for escape zone sizes determined. 13

14 Supplemental/poster slides 14

15 Test simulation: cusp field, small chamber, reduced energy ions: Coil Locations B (T) r (cm) R c =chamber radius=0 cm Particle energy scaling estimate: For R c =0 cm, assume maximum ion gyro-radius of (1/)*R c (use average B =0.5 T), then v ion ~ 0.03c for protons, or ~10 kev. Here I use 45 kev protons (directed energy) with a 1 kev thermal spread. 15

16 Simple cusp field for a 0-cm chamber, 45 kev protons: No self-field generation (Particle orbit calculations ONLY) Electrons Protons 0 ns 30 ns 10 ns 40 ns 0 ns 50 ns 16

17 60 ns 90 ns 70 ns 50 ns 80 ns 17

18 ~30% of the ion energy and charge remains after 50 ns. Ion Kinetic Energy Ion Charge 18

19 10 14 cm -3 plasma: (Detail of B and particles near center of chamber) 0 ns 5 ns 10 ns 19

20 Ion orbit calculation (no self-fields) cm initial radius 0 ns 300 ns 100 ns 400 ns 00 ns ~30% of the ions leave system after 600 ns. 500 ns 0

to fill in from self-consistent E-fields.

21 Full EM simulation with low initial plasma density: For an initial plasma density of 10 1 cm -3, ion orbit patterns begin to fill in from self-consistent E-fields. Small ion diamagnetic effects allow slightly deeper penetration into magnetic field. 1

22 β Simple estimate of stopping distance for expanding spherical plasma shell: nr ( ) mv i i ( r) ( ) 0 3 ( r) B 1 /µ ( 1/ ) i i 0 0 i i 0 c 5 B0 ( r/ Rc) Bor 1 nr n, for r 1cm B B0r r n r mv µ nmvµ R β = (in MKS units) Assuming plasma expansion stops for β ~ 1, then: 5 0 r stop = R c r stop nmv µ R 0 i i 0 c Bo 1/5 r stop (cm) This results is consistent with simulation results for n 0 = cm -3. v i = 0.01c B o = T protons n 0 (cm -3 )

23 A Look at Diamagnetic Plasma Penetration in 1D

24 1D EMHD model* The model assumes local charge neutrality everywhere. Electrons are cold, massless, and with a local ExB drift velocity Beam ions are kinetic, with an analytic perpendicular distribution function. Analysis is local, meaning that B o is approximately uniform with in the ion blob. Density v perp B o B 0 n b, n e *Adapted from K. Papadopoulos, et al., Phys. Fluids B 3, 1075 (1991). x 4

25 Model Equations: Ions Penetrating a Magnetized Vacuum Quasi-neutrality: Electron velocity: Continuity: Ion Distribution: Ion Density: Ion Pressure Force Balance: n ( x) = n ( x) b e ( ˆ ˆ) c u = E i + E k e z x By n e ue i = 0 B y H, ( ) Fb H = Mbv + eφ x Tb eφ nb( x) = nb0 Fb u+ du T 0 b eφ Pb( x) = nb0tb Fb u+ udu T 0 b P = n e E, E = φ b b 1 Pressure Balance: By + Pb = 8π 0 5

26 Magnetic field exclusion: Assume a perpendicular ion energy distribution given by: Assume a 1D density profile: Mv H b eφ Fb = exp T b T b T b x ne( x) = n exp b e0 The ion beam density and pressure are then given as: eφ n ( x) = n exp, P( x) = n ( x) T b b0 b b b Tb The potential and electric fields are then: Tb x T x φ ( x) =, E ( x) = eb e b b x From pressure balance, this gives a magnetic field profile of: 8π n et x By ( x) = B 1 exp b0 b 0 B0 b 1/ 6

27 Sample Result: B0 ( x) = x 5 µ n et By ( x) = B ( x) 1 exp ( x x ) 0 b0 b 0 0 B0 ( x) b 1/ (MKS units) b = 0.005; x0 = 1; nb0 = 1.0*10^(17)*(10^6); nb[x_] := nb0*exp[-((x - x0)^)/(b^)]/(x0^3); In the limit that the argument of the square root is > 0, this gives a simple diamagnetic reduction to the applied field. I assume that when the argument of the square root IS < 0, then the applied field is too wimpy to impede the drifting cloud. Plot[nb[x], {x, -0.0, *x0}, PlotRange -> {0, *nb0/(x0^3)}]; B0[x_] := (/5)*x; q = 1.6*10^(-19); Tb = (0.5*4*1.67*10^(-7)*((0.043*3*10^8)^))/q; mu0 = Pi*4*10^(-7); xmax = ((5/4)**mu0*nb0*q*Tb)^(1/5); Print["Tb(eV) = ", Tb]; Print["xmax (m) = ", xmax]; magdef01.nb magdef01.nb By[x_] := B0[x]*(Max[1 - *mu0*nb[x]*q*tb*(b0[x])^(-), 0])^(0.5); Plot[(By[x]), {x, 0, *x0}] 7

Penning Traps. Contents. Plasma Physics Penning Traps AJW August 16, Introduction. Clasical picture. Radiation Damping.

Penning Traps. Contents. Plasma Physics Penning Traps AJW August 16, Introduction. Clasical picture. Radiation Damping. Penning Traps Contents Introduction Clasical picture Radiation Damping Number density B and E fields used to increase time that an electron remains within a discharge: Penning, 936. Can now trap a particle